"""simple docstring"""


from dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
	from .features import FeatureType






@dataclass
class   __UpperCAmelCase		:
				A__ :  List[str]
				A__ :  Optional[str]    				=			None
				# Automatically constructed
				A__ :  ClassVar[str]    				=			"dict"
				A__ :  ClassVar[Any]    				=			None
				A__ :  str    				=			field(default='''Translation''' , init=__lowerCAmelCase , repr=__lowerCAmelCase      )

				def __call__( self ):
										return pa.struct({lang: pa.string() for lang in sorted(self.languages )} )






				def 						_a      ( self ):
										from .features import Value

										return {k: Value("string" ) for k in sorted(self.languages )}






@dataclass
class   __UpperCAmelCase		:
				A__ :  Optional[List]    				=			None
				A__ :  Optional[int]    				=			None
				A__ :  Optional[str]    				=			None
				# Automatically constructed
				A__ :  ClassVar[str]    				=			"dict"
				A__ :  ClassVar[Any]    				=			None
				A__ :  str    				=			field(default='''TranslationVariableLanguages''' , init=__lowerCAmelCase , repr=__lowerCAmelCase      )

				def 						_a      ( self ):
										lowerCamelCase__   =sorted(set(self.languages ) ) if self.languages else None
										lowerCamelCase__   =len(self.languages ) if self.languages else None

				def __call__( self ):
										return pa.struct({"language": pa.list_(pa.string() ), "translation": pa.list_(pa.string() )} )

				def 						_a      ( self      ,					_lowerCamelCase ):
										lowerCamelCase__   =set(self.languages )
										if self.languages and set(_lowerCamelCase ) - lang_set:
																raise ValueError(
																    F'''Some languages in example ({', '.join(sorted(set(_lowerCamelCase ) - lang_set ) )}) are not in valid set ({', '.join(_lowerCamelCase )}).''' )

										# Convert dictionary into tuples, splitting out cases where there are
										# multiple translations for a single language.
										lowerCamelCase__   =[]
										for lang, text in translation_dict.items():
																if isinstance(_lowerCamelCase      ,					_lowerCamelCase ):
																						translation_tuples.append((lang, text) )
																else:
																						translation_tuples.extend([(lang, el) for el in text] )

        # Ensure translations are in ascending order by language code.
										lowerCamelCase__   , lowerCamelCase__   =zip(*sorted(_lowerCamelCase ) )

										return {"language": languages, "translation": translations}






				def 						_a      ( self ):
										from .features import Sequence, Value

										return {
										    "language": Sequence(Value("string" ) ),
										    "translation": Sequence(Value("string" ) ),
										}



"""simple docstring"""


from __future__ import annotations

from typing import Any






class   __UpperCAmelCase		:

				def __init__( self      ,					_lowerCamelCase      ,					_lowerCamelCase      ,					_lowerCamelCase = 0 ):
										lowerCamelCase__   , lowerCamelCase__   =row, column
										lowerCamelCase__   =[[default_value for c in range(_lowerCamelCase )] for r in range(_lowerCamelCase )]

				def __str__( self ):
										lowerCamelCase__   =F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

										# Make string identifier
										lowerCamelCase__   =0
										for row_vector in self.array:
																for obj in row_vector:
																						lowerCamelCase__   =max(_lowerCamelCase      ,					len(str(_lowerCamelCase ) ) )
										lowerCamelCase__   =F'''%{max_element_length}s'''

										# Make string and return
										def single_line(_lowerCamelCase ) -> str:
																nonlocal string_format_identifier
																lowerCamelCase__   ="["
																line += ", ".join(string_format_identifier % (obj,) for obj in row_vector )
																line += "]"
																return line

										s += "\n".join(single_line(_lowerCamelCase ) for row_vector in self.array )
										return s

				def __repr__( self ):
										return str(self )

				def 						_a      ( self      ,					_lowerCamelCase ):
										if not (isinstance(_lowerCamelCase      ,					(list, tuple) ) and len(_lowerCamelCase ) == 2):
																return False
										elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
																return False
										else:
																return True

				def __getitem__( self      ,					_lowerCamelCase ):
										assert self.validate_indicies(_lowerCamelCase )
										return self.array[loc[0]][loc[1]]

				def __setitem__( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										assert self.validate_indicies(_lowerCamelCase )
										lowerCamelCase__   =value

				def __add__( self      ,					_lowerCamelCase ):
										assert isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										assert self.row == another.row and self.column == another.column

										# Add
										lowerCamelCase__   =Matrix(self.row      ,					self.column )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =self[r, c] + another[r, c]
										return result

				def __neg__( self ):
										lowerCamelCase__   =Matrix(self.row      ,					self.column )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =-self[r, c]
										return result

				def __sub__( self      ,					_lowerCamelCase ):
										return self + (-another)

				def __mul__( self      ,					_lowerCamelCase ):

										if isinstance(_lowerCamelCase      ,					(int, float) ):  # Scalar multiplication
																lowerCamelCase__   =Matrix(self.row      ,					self.column )
																for r in range(self.row ):
																						for c in range(self.column ):
																												lowerCamelCase__   =self[r, c] * another
																return result
										elif isinstance(_lowerCamelCase      ,					_lowerCamelCase ):  # Matrix multiplication
																assert self.column == another.row
																lowerCamelCase__   =Matrix(self.row      ,					another.column )
																for r in range(self.row ):
																						for c in range(another.column ):
																												for i in range(self.column ):
																																		result[r, c] += self[r, i] * another[i, c]
																return result
										else:
																lowerCamelCase__   =F'''Unsupported type given for another ({type(_lowerCamelCase )})'''
																raise TypeError(_lowerCamelCase )

				def 						_a      ( self ):
										lowerCamelCase__   =Matrix(self.column      ,					self.row )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =self[r, c]
										return result






				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										assert isinstance(_lowerCamelCase      ,					_lowerCamelCase ) and isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										assert self.row == self.column == u.row == v.row  # u, v should be column vector
										assert u.column == v.column == 1  # u, v should be column vector

										# Calculate
										lowerCamelCase__   =v.transpose()
										lowerCamelCase__   =(v_t * self * u)[0, 0] + 1
										if numerator_factor == 0:
																return None  # It's not invertable
										return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":





	def      lowerCamelCase_					(   )				->   None:




							'''simple docstring'''



							lowerCamelCase__   =Matrix(3  ,       3  ,       0							)
							for i in range(3							):
													lowerCamelCase__   =1
							print(F'''a^(-1) is {ainv}'''							)
							# u, v
							lowerCamelCase__   =Matrix(3  ,       1  ,       0							)
							lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =1, 2, -3
							lowerCamelCase__   =Matrix(3  ,       1  ,       0							)
							lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =4, -2, 5
							print(F'''u is {u}'''							)
							print(F'''v is {v}'''							)
							print(F'''uv^T is {u * v.transpose()}'''							)
							# Sherman Morrison
							print(F'''(a + uv^T)^(-1) is {ainv.sherman_morrison(__lowerCAmelCase  ,       __lowerCAmelCase							)}'''							)





	def      lowerCamelCase_					(   )				->   None:




							'''simple docstring'''



							import doctest

							doctest.testmod()





	testa()


